Problem: Simplify the following expression: $\dfrac{66t^5}{24t^2}$ You can assume $t \neq 0$.
$ \dfrac{66t^5}{24t^2} = \dfrac{66}{24} \cdot \dfrac{t^5}{t^2} $ To simplify $\frac{66}{24}$ , find the greatest common factor (GCD) of $66$ and $24$ $66 = 2 \cdot 3 \cdot 11$ $24 = 2 \cdot 2 \cdot 2 \cdot 3$ $ \mbox{GCD}(66, 24) = 2 \cdot 3 = 6 $ $ \dfrac{66}{24} \cdot \dfrac{t^5}{t^2} = \dfrac{6 \cdot 11}{6 \cdot 4} \cdot \dfrac{t^5}{t^2} $ $\phantom{ \dfrac{66}{24} \cdot \dfrac{5}{2}} = \dfrac{11}{4} \cdot \dfrac{t^5}{t^2} $ $ \dfrac{t^5}{t^2} = \dfrac{t \cdot t \cdot t \cdot t \cdot t}{t \cdot t} = t^3 $ $ \dfrac{11}{4} \cdot t^3 = \dfrac{11t^3}{4} $